📚 Magnetic Fields for IB and CIE Physics | IB CIE 物理磁场考点精讲
Magnetic fields are a fundamental topic in both IB and CIE A-Level Physics. Understanding how charges and currents interact with magnetic fields unlocks a wide range of phenomena, from the deflection of charged particles to the operation of motors and mass spectrometers. This article summarises the essential concepts, formulas, and applications you need for the exams.
磁场是 IB 和 CIE A-Level 物理中的基本课题。理解电荷和电流如何与磁场相互作用，可以揭示从带电粒子偏转到电动机、质谱仪运行等一系列现象。本文总结了你考试所需的核心概念、公式和应用。
1. Magnetic Fields and Field Lines | 磁场与磁感线
A magnetic field is a region of space where a moving charge or a magnetic material experiences a force. It is a vector field, denoted by B. Magnetic fields are produced by permanent magnets or moving charges (currents).
磁场是空间中移动电荷或磁性材料会受到力的区域。它是一个矢量场，用 B 表示。磁场由永磁体或移动电荷（电流）产生。
Field lines visualise the field. They emerge from north poles and enter south poles. The direction of the field at any point is tangent to the field line. The density of lines indicates field strength: closely spaced lines mean a stronger field.
磁感线可以形象地表示磁场。它们从北极出发，进入南极。某点的磁场方向为磁感线在该点的切线方向。磁感线的疏密表示场强：线越密，场越强。
In a uniform magnetic field, lines are parallel and equally spaced. This occurs inside a horseshoe magnet or between two flat magnetic poles.
在均匀磁场中，磁感线平行且等间距。这出现在马蹄形磁铁内部或两个平面磁极之间。
2. Magnetic Field due to a Current | 电流产生的磁场
A current-carrying straight wire generates a circular magnetic field around it. Use the right-hand grip rule: point your thumb in the direction of conventional current; your curled fingers show the direction of the magnetic field.
载流长直导线周围产生环形磁场。使用右手螺旋定则：拇指指向常规电流方向，弯曲的四指指示磁场方向。
The magnitude of the field at a distance r from a long straight wire in a vacuum is:
B = μ0 I / (2π r)
where μ0 = 4π × 10−7 T m A−1 is the permeability of free space.
真空中距长直导线 r 处的磁场大小为：B = μ0 I / (2π r)，其中 μ0 = 4π × 10−7 T m A−1 是真空磁导率。
For a solenoid of length L with N turns, the field inside is uniform and approximately:
B = μ0 n I
where n = N/L is the number of turns per unit length. The field outside is very weak.
对于长度为 L、匝数为 N 的螺线管，内部磁场近似均匀：B = μ0 n I，其中 n = N/L 是单位长度匝数。外部磁场非常弱。
3. Magnetic Flux and Flux Density | 磁通量与磁通密度
Magnetic flux Φ through a surface is defined as the product of the magnetic flux density B and the perpendicular area:
Φ = B A cos θ
flux density B is simply the magnetic field strength, measured in tesla (T); 1 T = 1 Wb m−2.
磁通量 Φ 定义为磁通密度 B 与垂直面积的乘积：Φ = B A cos θ，其中 θ 为磁场与表面法线的夹角。通量的单位是韦伯（Wb）。磁通密度 B 即磁场强度，单位为特斯拉（T）；1 T = 1 Wb m−2。
o the area, Φ = B A. When it is parallel, Φ = 0. Flux linkage for a coil of N turns is NΦ.
当磁场垂直于面积时，Φ = B A；平行时 Φ = 0。N 匝线圈的磁链为 NΦ。
4. Force on a Moving Charge (Lorentz Force) | 运动电荷所受的力（洛伦兹力）
A particle of charge q moving with velocity v in a magnetic field B experiences a force F = q v × B. In magnitude:
F = q v B sin θ
where θ is the angle between v and B. The direction is given by Fleming's left-hand rule (for positive charges): first finger field, second finger conventional current (velocity), thumb force. The force is always perpendicular to both v and B, so it does no work.
电荷 q 以速度 v 在磁场 B 中运动时，受力 F = q v × B。大小为 F = q v B sin θ，θ 为 v
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